Supply chain management (SCM) involves coordinating the flow of goods, information, and finances across various entities to deliver products efficiently. Effective inventory management is crucial in today's volatile, uncertain, complex, and ambiguous (VUCA) world. Previous research has demonstrated the superiority of heuristic methods and reinforcement learning applications in inventory management. However, the application of large language models (LLMs) as autonomous agents in multi-agent systems for inventory management remains underexplored. This study introduces a novel approach using LLMs to manage multi-agent inventory systems. Leveraging their zero-shot learning capabilities, our model, InvAgent, enhances resilience and improves efficiency across the supply chain network. Our contributions include utilizing LLMs for zero-shot learning to enable adaptive and informed decision-making without prior training, providing significant explainability and clarity through Chain-of-Thought (CoT), and demonstrating dynamic adaptability to varying demand scenarios while minimizing costs and avoiding stockouts. Extensive evaluations across different scenarios highlight the efficiency of our model in SCM.